Applying One-Dimensional TVD Scheme to Unstructured Mesh Finite Volume Solver


Adek Tasri


Mechanical Engineering Department, Universitas Andalas, Padang 25163, Indonesia.

Corresponding Author Email: adek.tasri@eng.unand.ac.id

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article discusses the application of the TVD limiter in the unstructured mesh finite volume solver used for fluid flow solutions. The application of the TVD limiter on an unstructured mesh is not straightforward as this type of mesh does not have clear directionality, so that the far upwind cells required for determining the successive gradient of the flow variable are not available. In this study, we used auxiliary points to replace the far upwind cell. The additional points were determined in such a way that it also acts as a spatial correction to minimize errors caused by unstructured mesh skewness. Numerical test, using two-dimensional advection of the scalar properties as test cases, showed that no spurious oscillations appear in some locations that have steep property gradients. TVD limiter with spatial correction gave relatively closer results to the exact value than TVD limiter without spatial correction. The application of the TVD limiter with the auxiliary points in the unstructured mesh successfully reduced oscillations in the numerical solution. At the same time, the spatial correction can reduce errors caused by mesh skewness.